Structured low-rank matrix / tensor approximation: numerical optimization-based algorithms and applications (SELMA)

Today's information society is centered on the collection of large amounts of data, from which countless applications aim at extracting information. They involve the manipulation of matrices and higher-order tensors, which can be viewed as large multi-way arrays containing numerical data. Key to their successful and efficient processing is the proper exploitation of available structure, and in particular low rank. This project aims to contribute innovative structure-exploiting methods based on the paradigm of low-rank matrix/tensor approximation, with a strong mathematical and algorithmic emphasis, and to apply them to large-scale data analysis, information retrieval and modelling. In WP 1, which supports and facilitates progress in the other WPs, we develop robust and computationally efficient algorithms for optimal low-rank approximation w.r.t. a given criterion, including algorithms that estimate the rank when not specified by the user. In WP2 we use low-rank approaches to tackle the fundamental problem of computing matrix products as cheaply as possible and to perform advanced curve fitting. In WP3 we develop large-scale structure-exploiting algorithms for nonnegative matrix factorization, a powerful tool to extract information from data, and for large-scale pattern recognition, which is at the heart of machine learning. Finally in WP 4 we exploit low-rank structure in the design of globally optimal methods for system identification, model reduction and signal processin